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In a lab frame of reference, an observer finds Newton’s second law is valid in the form
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Chapter 1 Solutions
Modern Physics
- Consider a particle of mass m acted on by a force F in an inertial frame. Prove that dK = F. dr, (1) where dr is the change in the position vector of the particle in a time dt, and dK is the corresponding change in the kinetic energy K = }mv².arrow_forwardHow do I answer this questionarrow_forwardAssertion (A): Any choice of an inertial frame is not acceptable in Newtonian Dynamics. Reason (R): The laws of motion are not equally valid in all such frames. (a) Both A and R are true, and R is the correct explanation of A (b) Both A and R are true, but R is not the correct explanation of A. (c) Both A and R are false. (d) A is false but R is true.arrow_forward
- An accelerated frame is a non-inertial frame A. true B. falsearrow_forwardThe coordinate axes of the reference frame S' remain parallel to those of S, as S' moves away from S at a constant velocity vs = (7.0î + 8.oĵ + 6.0k) m/s. (Express your answers in vector form. Use V the following as necessary: t. Assume all positions are in meters, velocities are in m/s, accelerations are in m/s2, and t is in seconds. Do not include units in your answers.) (a) If at time t = 0 the origins coincide, what is the position of the origin O' in the S frame as a function of time? O'(t) = (b) How is particle position for r(t) and r'(t), as measured in S and S', respectively, related? r(t) = r'(t) + (c) What is the relationship between particle velocities v(t) and v'(t)? v(t) = v'(t) + (d) How are accelerations a(t) and a'(t) related? a(t) = a'(t) +arrow_forwardA 300 m long train passed through a 500 m long tunnel. Both lengths are measured at rest. The train speeds at 4/5 c from west to east through the tunnel.In the tunnel's reference frame:i) What would be the length of the train?ii) What will be the time difference in seeing the end of the tunnel between Siti and Ahmad?arrow_forward
- R3B2. Alicia is a student on a passenger train moving at a constant velocity relative to the ground. She synchronizes her watch with the station clock as she passes through the town of Bannon station, and then compares her watch with the station clock as she passes through the Center town station farther down the line. The ground is an inertial frame, and the Bannon and Center clocks are synchronized in that frame. (1) Using a model or diagram, is the time she measures between the events of passing through these towns a proper time? (2) Is it a coordinate time in some inertial reference frame? (3) Is it the spacetime interval between the events?arrow_forwardShow that for two inertial reference systems Sand S' that move with a speed U with respect to Si, does the following equality hold? 22 (√²-√²³) = 22 (√²² - √:²³) Where Ve and Vo are the initial and final velocities in the S system and V'f and Vo are the initial and final velocities in the sl system and m is the mass of the particle. Under what conditions is equality fulfilled?arrow_forwardAn experimentalist in a laboratory finds that a particle has a helical path. The position of this particle in the laboratory frme is given by r(t)= R cos(wt)i + R sin(wt)j + vztk R,vz, and w are constants. A moving frame has velocity (Vm)L= vzk relative to the laboratory frame. In vector form: A)What is the path of the partical in the moving frame? B)what is the velocity of the particle as a function of time relative to the moving frame? C)What is the acceleration of the particle in each frame? D)How should the accelerartion in each frame be realted?Does your answer to part c make sense?arrow_forward
- R3M.8 The new earth-Pluto shuttle shuttle line boasts that it can take you between the two planets (which are about 5.0 hours of distance apart) in 2.5 hours (according to a rider’s watch). Assume that acceleration and deceleration periods are very brief so that you spend essentially all the trip traveling at a constant velocity. a) What time interval must synchronized clocks in the solar system’s reference frame register between the shuttle’s departure from earth and its arrival at Pluto if the advertisement is true? b) What is the shuttle’s cruising speed?arrow_forwardAn interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 74.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 19.4 years as measured in a rest frame. Note that radio waves travel at the speed of light and fill the space between the probe and Earth at the time the battery fails. (a) How long do the batteries on the space probe last as measured by mission control on Earth? (Ignore the delay between the time the battery fails and the time mission control stops receiving the signal.) yr (b) How far is the probe from Earth when its batteries fail as measured by mission control? (Ignore the delay between the time the battery fails and the time mission control stops receiving the signal.) ly (c) How far is the probe from Earth as measured by its built-in trip odometer when its batteries fail? ly (d) For what total time…arrow_forward4arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
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